3. Find the minimum and maximum values of f(x, y) = y2 – x² that lie on the circle x? + y? = 1 using Lagrange Multiplier. [ANS: Max. value = 1 and min. value = -1] 4. Find the minimum and maximum values of f(x,y) = y? – x² on the ellipse x² + 4y² = 4 using Lagrange Multiplier. [ANS: Max. value = 1 and min. value = -4]
3. Find the minimum and maximum values of f(x, y) = y2 – x² that lie on the circle x? + y? = 1 using Lagrange Multiplier. [ANS: Max. value = 1 and min. value = -1] 4. Find the minimum and maximum values of f(x,y) = y? – x² on the ellipse x² + 4y² = 4 using Lagrange Multiplier. [ANS: Max. value = 1 and min. value = -4]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![3. Find the minimum and maximum values of f(x,y) = y² – x² that lie on the circle x2 + y² = 1 using
Lagrange Multiplier.
[ANS: Max. value = 1 and min. value = -1]
%3D
4. Find the minimum and maximum values of f(x, y) = y2 - x² on the ellipse x2 + 4y² = 4 using
Lagrange Multiplier.
[ANS: Max. value = 1 and min. value = -4]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65a7e84b-5dfb-4495-9091-465e7e91bb23%2Fce746300-5bfc-4826-91cd-8f0e9c92e08b%2Fr7afvbb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Find the minimum and maximum values of f(x,y) = y² – x² that lie on the circle x2 + y² = 1 using
Lagrange Multiplier.
[ANS: Max. value = 1 and min. value = -1]
%3D
4. Find the minimum and maximum values of f(x, y) = y2 - x² on the ellipse x2 + 4y² = 4 using
Lagrange Multiplier.
[ANS: Max. value = 1 and min. value = -4]
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